Graphical models (GMs) are powerful statistical tools for modeling the (in)dependencies among random variables. In this paper, we focus on two different types of graphical models: R-vines and polytrees. Regarding the graphical representation of these models, the former uses a sequence of undirected trees with edges representing pairwise dependencies, whereas the latter uses a directed graph without cycles to encode independence relationships among the variables. The research problem we deal with is whether it is possible to build an R-vine that represents the largest number of independencies found in a polytree and vice versa. Two algorithms are proposed to solve this problem. One algorithm is used to induce an R-vine that represents in each tree the largest number of graphical independencies existing in a polytree. The other one builds a polytree that represents all the independencies found in the R-vine. Through simple examples, both procedures are illustrated.